If we keep clear of an advanced level, the wikipedia article on yeast is good. And has a good picture.

As far as I've been able to work out, Saccharomyces cerevisiae and most other yeast species reproduce asexually by budding. However, others as Schizosaccharomyces pombe do it by fission. This asexual stage is haploid.

Nutrient shortage triggers sexual reproduction. Haploid cells conjugate (diploid stage) and then perform meiosis giving four sexual haploid spores (sporulation). Traditional theory states that DNA recombination during meiosis helps withstand stress conditions by producing new gene combinations that probabilistacally increase the ability to cope with natural selection. However a more recent line of thinking suggests that meiosis might have evolved as a molecular mechanism to repair damage caused to DNA by high levels of environmental stress.

Please understand - there is no such thing as a "yeast species." Yeast is not a taxonmic classification - it's a morphology. It's generally assumed that any fungus can grow in that morphology under the right conditions and the morphology is not exlcusive to ploidy. We're most familiar with those fungi that exhibit the yeast mophology under routine culture conditions.